Title :

A quantitative central limit theorem for the effective conductance on the discrete torus

Author(s) :

Gloria, Antoine [Auteur]
Département de Mathématique [Bruxelles] [ULB]
Quantitative methods for stochastic models in physics [MEPHYSTO]
Nolen, James [Auteur]
Department of Mathematics [Durham]

Journal title :

Communications on Pure and Applied Mathematics

Pages :

2304--2348

Publisher :

Wiley

Publication date :

2016

ISSN :

0010-3640

English keyword(s) :

random conductance
CLT
variance estimate
stochastic homogenization

HAL domain(s) :

Mathématiques [math]/Probabilités [math.PR]
Mathématiques [math]/Analyse numérique [math.NA]
Mathématiques [math]/Equations aux dérivées partielles [math.AP]

English abstract : [en]

We study a random conductance problem on a d-dimensional discrete torus of size L>0. The conductances are independent, identically distributed random variables uniformly bounded from above and below by positive constants. ...
Show more >We study a random conductance problem on a d-dimensional discrete torus of size L>0. The conductances are independent, identically distributed random variables uniformly bounded from above and below by positive constants. The effective conductance AL of the network is a random variable, depending on L, and the main result is a quantitative central limit theorem for this quantity as L→∞. In terms of scalings we prove that this nonlinear nonlocal function AL essentially behaves as if it were a simple spatial average of the conductances (up to logarithmic corrections). The main achievement of this contribution is the precise asymptotic description of the variance of AL.Show less >

Language :

Anglais

Popular science :

Non

European Project :

QUANTHOM

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL